Laws of Text. Lecture Objectives. Text Technologies for Data Science INFR Learn about some text laws. This lecture is practical 9/26/2018

Transcription

1 Text Technologies for Data Science INFR11145 Laws of Text Instructor: Walid Magdy 26-Sep-2018 Lecture Objectives Learn about some text laws Zipf s law Benford s law Heap s law Clumping/contagion This lecture is practical 2 1

2 You can try with me Shell commands: cat, sort, uniq, grep Perl (or alternative) Excel (or alternative) Download the following: Bible: 3 Words nature Word basic unit to represent text Certain characteristics are observed for the words we use! These characteristics are very consistent, that we can apply laws for them These laws apply for: Different languages Different domains of text 4 2

3 Log(frequency) Frequency Frequency of words Some words are very frequent e.g. the, of, to Many words are less frequent e.g. schizophrenia, bazinga ~50% terms appears once Frequency of words has hard exponential decay Log(rank) 5 Zipf s Law: For a given collection of text, ranking unique terms according to their frequency, then: r P r const r, rank of term according to frequency P r, probability of appearance of term P r const r f x 1 x 6 3

4 Zipf s Law: Wikipedia abstracts 3.5M En abstracts r P r const r freq r const Term Rank Frequency the 1 5,134,790 of 2 3,102,474 in 3 2,607,875 a 4 2,492,328 is 5 2,181,502 and 6 1,962,326 was 7 1,159,088 to 8 1,088,396 by 9 766,656 an ,970 it ,492 for ,374 as ,277 on ,544 from ,785 r x freq 5,134,790 6,204,948 7,823,625 9,969,312 10,907,510 11,773,956 8,113,616 8,707,168 6,899,904 5,669,700 6,132,412 5,970,456 6,413,862 6,723,878 7,073,160 7 Distribution of first digit in frequencies? 1) Uniform 2) Exp decay 3) Normal Term Rank Frequency the 1 5,134,790 of 2 3,102,474 in 3 2,607,875 a 4 2,492,328 is 5 2,181,502 and 6 1,962,326 was 7 1,159,088 to 8 1,088,396 by 9 766,656 an ,970 it ,492 for ,374 as ,277 on ,544 from ,

5 v (vocabulary) Benford s Law: First digit of a number follows a Zipf s like law! Terms frequencies Physical constants Energy bills Population numbers Benford s law: P d = log(1 + 1 d ) 9 Heap s Law: While going through documents, the number of new terms noticed will reduce over time For a book/collection, while reading through, record: n: number of words read v: number of news words (unique words) Vocabulary growth: v n = k n b where, b < 1 typically, 0.4 < b < 0.7 n (words) 10 5

6 Heap s Law: shouldn t it saturate? n = 80+ million, but still growing Think about: - spelling errors - names - s - codes Accurate for most collections, but different k, b Not very accurate when n is small 11 Clumping/Contagion in text From Zipf s law, we notice: Most words do not appear that much! Once you see a word once expect to see again! Words are like: Rare contagious disease Not, rare independent lightening Words are rare events, but they are contagious 12 6

7 density Clumping/Contagion in text Wiki abstract collection Identify terms appeared only twice Measure distance between the two occurrences of the terms: d = n occurence2 n occurence1 Plot density function of d Majority of terms appearing only twice appear close to each other. distance (d) 13 Applying the laws Given a collection of 20 billion terms, What is the number of unique terms? Heap s law: v n = k n b, assume k = 0.25, b = 0.5 v n = 0.25 (20B) M What is the number of terms appearing once? Zipf s law ~17M appeared only once 14 7

8 Summary Text follows well-known phenomena Text Laws: Zipf Heap Contagion in text 15 Recourses Text book: Search engines: IR in practice chapter 4 Videos: Zipf s law, Vsouce: Benford s law, Numberphile: Tools: Unix commands for windows